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# 420Hw02ans - STAT 420 Spring 2010 Homework#2(12 points(due...

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STAT 420 Spring 2010 Homework #2 (12 points) (due Friday, February 5, by 4:00 p.m.) 1. 4.9 Do NOT use a computer for this problem A transportation analyst wishes to compare the “degree of support” for a new rapid transit system among the following three groups of people in the Madison, Wisconsin, area: group A, University of Wisconsin faculty; group B, downtown businessmen; and group C, state government personnel. A questionnaire was designed from which a “rapid transit support index” could be computed for each respondent. The questionnaire was given to randomly selected people from each group. The results follow. Rapid Transit Support Index Group A B C 66 59 70 65 76 84 45 53 62 72 78 50 57 49 61 53 72 80 Stating any assumptions you make, test for differences between the three populations represented by the three samples using the F test. Specify the null and the alternative hypotheses. Show the calculations leading to your conclusion in the form of an ANOVA table. (You should be able to calculate easily all the ANOVA table entries given the following summary measures: J = 3, n = 6, A Y = 70, B Y = 60, C Y = 62, 2 A s = 78.8, 2 B s = 169.2, 2 C s = 140.0.) N = n A + n B + n C = 6 + 6 + 6 = 18 . 18 1152 18 62 6 60 6 70 6 = = Y = 64 .

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SSB = ( ( ( 2 2 2 Y Y n Y Y n Y Y n C C B B A A - + - + - = 6 ( 70 – 64 ) 2 + 6 ( 60 – 64 ) 2 + 6 ( 62 – 64 ) 2 = 216 + 96 + 24 = 336 . MSB = 2 336 1 SSB = - J = 168 . SSW = ( ( ( 2 2 2 1 1 1 C C B B A A s n s n s n - + - + - = 5 78.8 + 5 169.2 + 5 140.0 = 394 + 846 + 700 = 1940 . MSW = 15 1940 SSW = - J N 129.3333 . SSTot = SSB + SSW = 336 + 1940 = 2276 . F = 3333 . 129 168 MSW MSB 1.29897 . ANOVA table: Source SS DF MS F Between 336 2 168 1.29897 Within 1940 15 129.3333 Total 2276 17 F 0.05 ( 2, 15 ) = 3.68 . Do NOT Reject H 0 : μ A = μ B = μ C at α = 0.05. F 0.10 ( 2, 15 ) = 2.70 . Do NOT Reject H 0 : μ A = μ B = μ C at α = 0.10. p-value = [ = FDIST ( 1.29897 , 2 , 15 ) ] = 0.3018 . > 1-pf(1.29897,2,15) [1] 0.301801
2. The friendly folks at the Internal Revenue Service (IRS) are always looking for ways to improve the wording and format of its tax return forms. Three new forms have been developed recently. To determine which, if any, are superior to current form, 120 individuals were asked to participate in an experiment. Each of the three new forms and the currently used form were filled out by 30 different people. The amount of time (in minutes) taken by each person to complete the task was recorded and stored in columns 1 through 4 (forms Form1 through Form4, respectively) in file Hw02_2.csv. The data set is available at http://www.stat.uiuc.edu/~stepanov/Hw02_2.csv To create a data frame in R, use Hw02_2 = read.table("http://www.stat.uiuc.edu/~stepanov/Hw02_2.csv", sep=",", header=T) sep="," indicates that the data in the data file are separated by a comma, header=T indicates that the first line of the data file contains the names for the variables (as opposed to header=F ) You can then access individual variables in the data frame Hw02_2 by using Hw02_2\$Form1 , Hw02_2\$Form2 , Hw02_2\$Form3 , and Hw02_2\$Form4 .

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